Cosecant of 300 Degrees
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Theorem
- $\csc 300^\circ = \csc \dfrac {5 \pi} 3 = -\dfrac {2 \sqrt 3} 3$
where $\csc$ denotes cosecant.
Proof
| \(\ds \csc 300^\circ\) | \(=\) | \(\ds \csc \left({360^\circ - 60^\circ}\right)\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds -\csc 60^\circ\) | Cosecant of Conjugate Angle | |||||||||||
| \(\ds \) | \(=\) | \(\ds -\frac {2 \sqrt 3} 3\) | Cosecant of 60 Degrees |
$\blacksquare$
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Exact Values for Trigonometric Functions of Various Angles